To answer your main question, yes you can use your binding on a straight edge. Just be careful not to stretch it too tight if it is cut on the bias. I was taught to just cut my binding fabric across the width of the fabric and it has always worked fine for me.
As for mitering the corners,(1) Sew to within 1/4" of the edge of the quilt, stop.(2) Raise presser foot and swivel quilt as if to continue along the next side.(3) Now reverse stitch so you are off the quilt.(4) Fold fabric back on itself at a 45* angle from corner. (5) Now bring fabric forward and lie along side to be sewn, while keeping miter in place with left hand (or right hand if you are left handed) Not as hard as it sounds. That's all there is too it.